What is the diameter (in cm). of a sphere of surface area 6.16 sq. cm ?

Options

A. `1.4`
B. `0.7`
C. `2.8`
D. `2.1`

Answer

To find the diameter of a sphere given its surface area, we can follow these steps:

### Step 1: Write the formula for the surface area of a sphere.
The surface area \( A \) of a sphere is given by the formula:
\[ A = 4\pi r^2 \]
where \( r \) is the radius of the sphere.

### Step 2: Substitute the given surface area into the formula.
We know the surface area \( A = 6.16 \) sq. cm. So we can set up the equation:
\[ 6.16 = 4\pi r^2 \]

### Step 3: Solve for \( r^2 \).
First, we can isolate \( r^2 \) by dividing both sides by \( 4\pi \):
\[ r^2 = \frac{6.16}{4\pi} \]
Now, we can substitute \( \pi \) with \( \frac{22}{7} \):
\[ r^2 = \frac{6.16}{4 \times \frac{22}{7}} = \frac{6.16 \times 7}{88} \]

### Step 4: Calculate the value of \( r^2 \).
Calculating the numerator:
\[ 6.16 \times 7 = 43.12 \]
Now, divide by 88:
\[ r^2 = \frac{43.12}{88} = 0.49 \]

### Step 5: Find \( r \) by taking the square root of \( r^2 \).
\[ r = \sqrt{0.49} = 0.7 \text{ cm} \]

### Step 6: Calculate the diameter \( d \).
The diameter \( d \) is twice the radius:
\[ d = 2r = 2 \times 0.7 = 1.4 \text{ cm} \]

### Final Answer:
The diameter of the sphere is \( 1.4 \) cm.

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